# Memory-Guided Tree Search with Cross-Branch Knowledge Transfer for LLM Solver Synthesis

arXiv: https://arxiv.org/abs/2605.17539 · HTML: https://mlsanity.com/paper/2605.17539/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 34 references that are in the map.
- First posted on arXiv 17 May 2026.

## Builds on (most cited first, 24 of 24)

- [Reflexion: Language Agents with Verbal Reinforcement Learning](https://mlsanity.com/paper/2303.11366/) (2023)
- [Generative Agents: Interactive Simulacra of Human Behavior](https://mlsanity.com/paper/2304.03442/) (2023)
- [Self-Refine: Iterative Refinement with Self-Feedback](https://mlsanity.com/paper/2303.17651/) (2023)
- [Tree of Thoughts: Deliberate Problem Solving with Large Language Models](https://mlsanity.com/paper/2305.10601/) (2023)
- [Voyager: An Open-Ended Embodied Agent with Large Language Models](https://mlsanity.com/paper/2305.16291/) (2023)
- [Machine Learning for Combinatorial Optimization: a Methodological Tour d'Horizon](https://mlsanity.com/paper/1811.06128/) (2018)
- [Neural Combinatorial Optimization with Reinforcement Learning](https://mlsanity.com/paper/1611.09940/) (2016)
- [Learning Combinatorial Optimization Algorithms over Graphs](https://mlsanity.com/paper/1704.01665/) (2017)
- [POMO: Policy Optimization with Multiple Optima for Reinforcement Learning](https://mlsanity.com/paper/2010.16011/) (2020)
- [ReEvo: Large Language Models as Hyper-Heuristics with Reflective Evolution](https://mlsanity.com/paper/2402.01145/) (2024)
- [An Efficient Graph Convolutional Network Technique for the Travelling Salesman Problem](https://mlsanity.com/paper/1906.01227/) (2019)
- [Evolution of Heuristics: Towards Efficient Automatic Algorithm Design Using Large Language Model](https://mlsanity.com/paper/2401.02051/) (2024)
- [LEVER: Learning to Verify Language-to-Code Generation with Execution](https://mlsanity.com/paper/2302.08468/) (2023)
- [AIDE: AI-Driven Exploration in the Space of Code](https://mlsanity.com/paper/2502.13138/) (2025)
- [Sym-NCO: Leveraging Symmetricity for Neural Combinatorial Optimization](https://mlsanity.com/paper/2205.13209/) (2022)
- [OptiMUS: Scalable Optimization Modeling with (MI)LP Solvers and Large Language Models](https://mlsanity.com/paper/2402.10172/) (2024)
- [Monte Carlo Tree Search for Comprehensive Exploration in LLM-Based Automatic Heuristic Design](https://mlsanity.com/paper/2501.08603/) (2025)
- [Learning the Travelling Salesperson Problem Requires Rethinking Generalization](https://mlsanity.com/paper/2006.07054/) (2020)
- [Augmenting Operations Research with Auto-Formulation of Optimization Models from Problem Descriptions](https://mlsanity.com/paper/2209.15565/) (2022)
- [Autoformulation of Mathematical Optimization Models Using LLMs](https://mlsanity.com/paper/2411.01679/) (2024)
- [CO-Bench: Benchmarking Language Model Agents in Algorithm Search for Combinatorial Optimization](https://mlsanity.com/paper/2504.04310/) (2025)
- [OptiTree: Hierarchical Thoughts Generation with Tree Search for LLM Optimization Modeling](https://mlsanity.com/paper/2510.22192/) (2025)
- [Coarse-to-Fine Grounded Memory for LLM Agent Planning](https://mlsanity.com/paper/2508.15305/) (2025)
- [ORMind: A Cognitive-Inspired End-to-End Reasoning Framework for Operations Research](https://mlsanity.com/paper/2506.01326/) (2025)

## Built on by (most cited first, 1 of 1)

- [Operator Packages, Proposer Strength, and Construction-Family Plateaus in Office-Scale Verified Search](https://mlsanity.com/paper/2609.29636/) (2026)

## Abstract (arXiv)

Combinatorial optimization (CO) underlies decision-making from logistics to chip design, where infeasible solutions are operationally unusable and small quality gains translate into substantial economic value. Recent work uses large language models (LLMs) to automate solver synthesis: generating executable solver programs from natural-language specifications. However, existing tree-search and evolutionary agents refine candidate trajectories in parallel without explicit knowledge transfer, reintroducing the same constraint violations and converging on similar algorithm families. We introduce MEMOIR, a memory-guided tree-search framework with a two-level memory hierarchy: branch-local memory preserves execution-grounded refinement details within a branch as it iterates on a single algorithmic design, while global memory stores compressed algorithmic and failure-mode summaries across branches. A reflection step at branch termination distills these summaries, enabling cross-branch transfer without polluting future contexts with low-level debugging traces. Across seven CO problems spanning scheduling, routing, packing, and geometric design, MEMOIR achieves 96.7% solution validity (a 9.2 point gap over the strongest baseline) and improves the average normalized score by 7.3 points at matched per-method execution budget. Over three independent runs on four problems, MEMOIR's run-to-run validity standard deviation is more than an order of magnitude below that of every baseline we evaluated in this setting, suggesting that memory-guided exploration yields consistent improvements rather than reflecting sampling variance.